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ESOC commenced its activities to establish an ionosphere monitoring tool, based on the routine processing of International GNSS Service (IGS)/GPS dual-frequency data, in 1993. Mathematical models as well as dedicated software had to be established from scratch. Based on comprehensive literature studies, in a first step all mathematical basics, such as TEC observables computation, geomagnetic coordinates, coordinate and time transformations, solar and spacecraft ephemeris, vector methods for ionospheric intersection point computation, mapping functions, parameter estimation algorithms etc. were put together. At the end of 1995, a prototype version of the new ionosphere monitoring software was ready, representing the ionospheric vertical Total Electron Content (vTEC) as single layer. This prototype version was quasi-operationally used since 1996 and became, after some further upgrades, fully operational as IONosphere MONitoring Facility (IONMON) Version 1 in 1998.

Since 1997, also first steps were undertaken into the direction of a 3D modeling of the ionosphere, and already IONMON Version 1 offered, apart from single layer approaches, a first Chapman Profile-based 3D model.

In 1999, efforts started to extend the 3D Chapman Profile approach of 1997 to a multilayer 3D ionosphere model. Also this work included the development of comprehensive new mathematical models (Ref. [5]) and software: different types of profile functions, empirical model for height-dependent scale height, dedicated TEC integrator and many others. This so-called IONMON Version 2 is available since March 2008. In addition to TEC derived from dual-frequency IGS/GNSS data, IONMON Version 2 needs observed electron density profiles, e.g. from COSMIC or ionosonde, for its 3D processing. The basic concept of IONMON Version 2 is to combine surface functions representing the horizontal variation of key profile parameters, such as maximum electron densities and peak heights, with profile functions describing the vertical structure of the ionosphere.

IONMON Version 2 is still in an experimental phase and the test results showed that its performance is not as expected (Refs. [1], [6]). In spite of including electron density data in addition to the GNSS-derived TEC data, the global observation data coverage is still too sparse to obtain reliable 3D pictures of the ionosphere by least squares fits. Instead, IONMON Version 2 has to be underpinned with a background model combined with an observation data assimilation. A concept for this upgrade was recently worked out and documented in a technical note. Currently the related software upgrades are under preparation.

IONMON Version 1 and IONMON Version 2 will be described in more detail in the following sections. All the algorithms used by IONMON Version 1 and IONMON Version 2, including the planned upgrades of IONMON Version 2, are documented in several comprehensive ESOC-internal technical notes.

 For details about ESOC’s routine ionosphere processing see Ionosphere Webpage.


IONMON Version 1 is a well developed single layer model being operationally used for the ESA contributions to the IGS Ionosphere Working Group since 1998 as well as for the support of in-house missions. Among different surface functions, spherical harmonics turned out to be best suited for global single layer TEC representations. The IONMON Version 1 approach is very similar to the Center for Orbit Determination in Europe, Astronomical Institute of the University of Berne, Berne, Switzerland (CODE) approach, providing TEC maps with comparable accuracy. The spherical harmonics resolution set in processing is degree and order 15. Together with the spherical harmonic coefficients to represent the vTEC, per satellite and station a Differential Code Bias (DCB) value is estimated. In order to avoid a singularity in the normal matrix, the DCB value of one station or one satellite is arbitrarily kept fixed with zero. After the estimation process, all DCBs, station and satellite, are referred to the mean over all satellites.

The estimation process (Ref. [4]) can in short be summarized as follows: vTEC maps and (unofficial) DCB values are estimated in a sequential estimation process in a 2-hours update rate. To the normal matrix of the actual 2 hours a weight matrix is added. This weight matrix is composed of the normal matrices of the previous updates summed up with exponentially in time decaying weights, i.e. the older the normal matrix, the less its weight in the weight matrix. For the (official) DCBs, all normal equations that accumulated during one day are added together with equal weight, and the resulting normal equation system is solved to obtain the daily set of (official) DCBs. The vTEC maps of the 2-hourly sequential updates of one day and the daily set of DCBs are finally merged together to the ESA IONEX file for that day for delivery to the IGS.

Currently, 1-hour updates are run in parallel to the 2-hours updates in an experimental phase and will replace the 2-hours updates in future. Test runs with a 15-minutes update interval were also successful, Figure 1.

Figure 1 displays an IONMON Version 1 vTEC film for 22 – 28 March 2011 obtained from 15-minutes updates.


Figure 1: vTEC film displaying the ionosphere from 22 – 28 March 2011 in 15-minutes resolution, computed with IONMON Version 1 


While many other approaches to model the ionosphere are purely empirical, like the single layer approaches described above on the example of IONMON Version 1, or the tomography models, the intension of the IONMON Version 2 concept was to include some very simple physical features into the model (Ref. [5]), in this way allowing to a limited extent for some physical interpretations of the model output: Thus, instead of subdividing the ionosphere into grids or voxels, it was decided to describe the ionosphere’s vertical electron density structure by compositions of elementary profile functions accounting for the different ionospheric layers. This concept follows basically the principle of Ching and Chiu (Refs. [2}, [3]): Each profile function has its key parameters, such as maximum electron density, height of maximum electron density and scale height. In IONMON Version 2 these key parameters are in turn expressed by global surface functions, whose coefficients are then estimated, in this way describing the horizontal variations of the ionosphere.

Several profile functions were worked out for the IONMON Version 2, which might be subdivided into two major categories: 1) Purely empirical, such as Hyperbolic Secant-like, and 2) Chapman Profile-based. In addition, IONMON Version 2 comprises dedicated algorithms for many other aspects of 3D ionosphere modeling, such as height-dependent scale height, special TEC integrator, plasmasphere, … . Beyond GNSS-derived TEC, also observed electron density data, e.g. from COSMIC and ionosondes, are processed in IONMON Version 2.

Category 2) of the IONMON Version 2 profile functions were designed in such a way that the analysis of their estimated key parameters may allow for some physical interpretations. If the standard Chapman Profile is for instance used, key parameters, namely maximum electron density, height of maximum electron density, scale height and recombination coefficient, can be estimated (or combinations where some of these parameters are estimated while the others are kept fixed). The standard Chapman Profile has a fixed topside/bottomside ratio of electron density. By combining the standard Chapman Profile function with its mirrored counterpart, this top/bottomside ratio can be modified, e.g. when estimating the combination coefficient  between original function and mirrored counterpart. Figure 2 shows the resulting curves of different levels of combination  of the standard Chapman Profile with its mirrored counterpart.

Figure 2: Profile functions obtained by combining the Chapman Profile function with its mirrored counterpart for     0 ≤ L ≤ 1

The fitted profile function might then be interpreted as being composed of (1-L)  % of a standard Chapman Profile and  L % of its mirrored counterpart, with related physics.

In an analogous way, corrections can be estimated to the coefficients of the Chapman Profile MacLaurin series expansion (Ref. [5]), Figure 3.

Figure 3: Examples showing observed Champ electron densities (red dots) versus the fitted series expansion (green line) for some arbitrarily selected Champ profiles

The benefit of the Chapman Profile MacLaurin series expansion is that all ionospheric layers can be covered by one series expansion fit, Figure 3. In addition, with the series expansion integral, the TEC over all layers can easily be computed. A disadvantage of the series expansion is that its convergence region is limited to the central part of the ionosphere. At the top and at the bottom, the series expansion has therefore to be supplemented with empirical exponential functions, similar to a plasmaspheric correction.

A systematic fit of Chapman Profile MacLaurin series expansions to many observed electron density profiles and a systematic analysis of estimated coefficients may reveal typical signatures depending on solar cycle, geomagnetic latitude, season and daytime. A systematic analysis of these coefficients, fitted under different ionospheric conditions, may therefore allow for a physical interpretation of ionospheric behaviour, in a similar way as is done with low degree and order spherical harmonic coefficients for the earth gravity field for example.

In addition to the IONMON Version 2 software, a small prototype tool for making single PROfile FITs (PROFIT) has been established. Perhaps PROFIT might be upgraded to an operational software in future. The Chapman Profile MacLaurin series expansion fits shown in Figure 3 were actually made with PROFIT.

Test runs revealed that the IONMON Version 2 performance is not as expected (Refs. [1], [6]). The system needs to be upgraded with a background model and an observation data assimilation. Reasons and details are described in Section 4.


IONMON Version 2 is based on closed functions to describe the ionosphere in its horizontal as well as its vertical structures. From their nature, such closed functions, e.g. spherical harmonics and Chapman Profiles, are not as flexible as voxel approaches. In a tomographic model, each voxel can be updated independently of the other voxels. Therefore, tomographic approaches are in general more flexible and adaptable than closed function approaches. On the other hand, closed function representations allow the computation of the ionosphere’s state at any point in space, interpolation is not necessary and related interpolation errors can be avoided.

IONMON Version 2 has, in its current setup, no background model but relies purely on as many observation data as possible into which the 3D model is fitted. In spite of using at the moment TEC data from about 300 globally distributed IGS sites and up to 2500 COSMIC profiles per day, global data coverage is still (and will remain) sparse, especially over the ocean regions. Thus the concept of a least squares fit of observation data (over determined problem) into a 3D model has to be replaced by a background model combined with a least squares interpolation (under determined problem) based data assimilation. A new strategy for upgrading the IONMON Version 2 with a background model and a data assimilation was recently worked out and documented in a technical note. Now, the corresponding software modifications and extensions are under preparation. The planned 3D model and related software upgrades comprise:

  • 3D background model of the ionosphere: This background model will describe the maximum electron density N0, and in a later step also the peak height h0, with empirical formulae in closed form for the global ionosphere and be based on algorithms from the German Aerospace Center (DLR), Institute of Communications and Navigation, Neustrelitz, Germany (Ref. [8]). The profile parameters N0 and h0 will then be used, together with appropriate scale heights and a recombination coefficient of ½, to describe the ionosphere’s vertical electron density distribution by one perfect Chapman Profile. In a further step of development, two Chapman Profiles, one for the F-layer and one for the E-layer, might be introduced into the background model.
  • Observation data assimilation (TEC and electron densities) will be based on a least squares interpolation or a simplified equivalent approach.
  • DCBs will have to be entered from an external source into the system, e.g. by either taking IGS IONEX values, or by performing a single layer fit for the day before with IONMON Version 1 and predicting these DCB values to the day to be processed.
  • The Chapman Profile MacLaurin series expansion, when fitted to observed electron density profiles, is able to adapt to structures in the observed electron density profiles, which are so small that these structures can at the moment not reliably be interpreted as being really existent, i.e. the series expansion is able to represent details which are currently not yet reliably observable. Therefore it was decided not to include the Chapman Profile MacLaurin series expansion in the background model for the time being, but in future, with more sensitive observation techniques, it may become relevant. Nevertheless, upgrades of the Chapman Profile MacLaurin series expansion are foreseen for a better numerical conditioning and for the masking of the divergence regions at the top and at the bottom of the series expansion profile function.
  • Background model and data assimilation are designed so, that they shall also allow for Near-Real-Time and Real-Time processing.

Before being upgraded, the IONMON will, in its current setup, be integrated into the ESOC’s NAPEOS software, and then the upgrades will be made to IONMON once being part of NAPEOS. Currently, this integration of the IONMON into NAPEOS is under work. In addition, NAPEOS was recently enabled to compute the so-called higher order ionospheric terms (e.g. Ref. [7]).


ESOC’s Navigation Support Office commenced its activities in the area of the ionosphere in 1993. In 1996 a prototype version of an ionosphere monitoring system became quasi-operational and, after some further upgrades, fully operational as IONosphere MONitoring Facility (IONMON) Version 1 in 1998. While IONMON Version 1 is based on a so-called single layer approach, in 1997 first steps were already undertaken for a 3D modeling of the ionosphere, resulting in a first Chapman Profile-based 3D model. In 1999 efforts started to extend this 3D Chapman Profile approach to a multilayer 3D ionosphere model resulting in IONMON Version 2. IONMON Version 2 uses a closed function approach describing the 3D ionosphere by means of vertical profile functions combined with horizontal surface functions and processes TEC observables together with observed electron densities.

Test runs revealed that IONMON Version 2 in its current setup is hardly able to reproduce the 3D ionosphere with the currently available amount and distribution of observation data, and it cannot be expected that global data coverage will significantly improve in foreseeable future. Thus, upgrades of the current IONMON Version 2 system have been worked out and are now under preparation for inclusion into the software:

–         Inclusion of a background model combined with an observation data assimilation

–         Enabling of Near-Real-Time and Real-Time processing capability

–         Optimization of existing algorithms

Before these upgrades will be made, the IONMON will be integrated the ESOC’s NAPEOS software.


[1] DOPS-SYS-RP-5001-OPS-GN: Recommendations for a New European Ionosphere Monitoring System, Iss. 1/0, 20/01/2010.

[2] Ching, B. K. and Y. T. Chiu (1973): “A phenomenological model of global ionospheric electron density in the E-, F1- , and F2-regions”, J Atmos Terr Phys, 35, 1615

[3] Chiu, Y. T. (1975): “An improved phenomenological model of ionospheric density”, J Atmos Terr Phys, 37, 1563-1570

[4] Feltens, J. and J. Dow, (2006): „Realized and Planned Improvements in ESA/ESOC Ionosphere Modelling”, IGS Presentation, in Proceedings of the 2006 IGS Workshop, ESOC, Darmstadt, May 8-11, 2006.

[5] Feltens, J. (2007), “Development of a new three-dimensional mathematical ionosphere model at European Space Agency/European Space Operations Centre”, Space Weather, 5, S12002, doi:10.1029/2006SW000294.

[6] Feltens, J., M. Angling, N. Jackson-Booth, N. Jakowski, M. Hoque, M. Hernández-Pajares, A. Aragón-Angel, R. Orús and R. Zandbergen (2011): “Comparative testing of four ionospheric models driven with GPS measurements”, Radio Science, 2010RS004584, accepted, in preparation for print.

[7] Hoque, M.M. and N. Jakowski (2008): ‘Estimate of higher order ionospheric errors in GNSS positioning’, Radio Science, Vol. 43, RS5008, doi: 10.1029/2007RS003817, 2008.

[8] Jakowski, N., M.M. Hoque and C. Mayer(2011): ‘A new global TEC model for estimating transionospheric radio wave propagation errors, J Geod (2011) 85:965-974, doi: 10.1007/s00190-011-0455-1.